$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 6x + 5$ and $ BC = 5x + 8$ Find $AC$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {6x + 5} = {5x + 8}$ Solve for $x$ $ x = 3$ Substitute $3$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 6({3}) + 5$ $ BC = 5({3}) + 8$ $ AB = 18 + 5$ $ BC = 15 + 8$ $ AB = 23$ $ BC = 23$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {23} + {23}$ $ AC = 46$